Bond accrued interest is accrued interest as it applies to bonds: the portion of the next coupon that has been earned, but not yet paid, between the last coupon date and the settlement date of a trade. Because the issuer pays the whole coupon to whoever holds the bond on the record date, a buyer compensates the seller for the days the seller held it. The amount is added to the quoted "clean" price to give the "dirty" price actually paid.
The calculation multiplies the coupon rate by the nominal amount and by the fraction of the coupon period that has elapsed. How that fraction is counted depends on the bond's day count convention, which differs between government, corporate and money market instruments. Accrual runs up to, but does not include, the settlement date.
Some bonds trade without accrued interest, for example bonds in default. In a short period before each coupon payment, certain markets trade bonds ex-coupon, and accrued interest is then negative. Its role in valuation is explained under bond pricing.